Figures REF (a) and REF (b) show the derivative \(dM/dH_x\)  vs \(H_x\)  in the \(ab\)  plane for EuMg\(_2\) Bi\(_2\)  and EuMg\(_2\) Sb\(_2\)  obtained from the data in Figs. REF (a) and REF (b), respectively. The data exhibit maxima in \(dM/dH_x\)  which yield \(H_{\rm c1}=465\)  Oe for EuMg\(_2\) Bi\(_2\)  and 220 Oe for EuMg\(_2\) Sb\(_2\) , respectively. Then using the value \(\chi _{ab}(T_{\rm N}) = 1.31\)  cm\(^{3}\) /mol from Fig. 5(a) of Ref. [1]} which is the same as the value of the high-field derivative at \(H_{\rm c1} \approx 465\)  Oe in Fig. REF (a), the value of \(K_3\)  is obtained from Eq. (REF ) for EuMg\(_2\) Bi\(_2\) . Similarly, for EuMg\(_2\) Sb\(_2\)  \(\chi _{ab}(T_{\rm N}) = 1.58\)  cm\(^{3}\) /mol and \(H_{\rm c1} \approx 220\)  Oe. The results for the respective trigonal anisotropy constants are
\(K_3 &=& 1.0\times 10^{-19}~{\rm erg/Eu} \quad ({\rm EuMg_2Bi_2}) \\&=& 6.5\times 10^{-8}~{\rm eV/Eu},\nonumber \\K_3 &=& 2.8\times 10^{-20}~{\rm erg/Eu} \quad ({\rm EuMg_2Sb_2})\\&=& 1.8\times 10^{-8}~{\rm eV/Eu}.\nonumber \) 
